HALDANE ON SELECTION 



By LOWELL J. REED 



School of Hygiene and Public Health, Johns Hopkins University 

 (Paper No. 141 from The Department of Biometry and Vital Statistics) 



THE modern theories of inherit- 

 ance are sufficiently definite to 

 tempt the mathematically in- 

 clined to subject them to an- 

 alysis for the sake of determining the 

 consequences that flow from them. Pear- 

 son (1), Warren (z), Norton (3), and 

 Jennings (4) have dealt with certain 

 phases of the problem, but by far the 

 most thoroughgoing treatment has been 

 given in a series of papers by J. B. S. 

 Haldane (5). The present article is a 

 review of the method of approach and the 

 results obtained in this excellent series of 

 papers. 



The author has defined the general 

 problem by stating that when given (1) 

 the mode of inheritance of the character 

 considered, (z) the system of breeding in 

 the group of organisms studied, (3) the 

 intensity of selection, (4) its incidence 

 (that is, on both sexes or only one), it 

 should be possible to state the value of 

 (5) the rate at which the proportion of 

 organisms showing the character in- 

 creases or diminishes, in terms of (3) the 

 intensity of selection. Conditions (1), 

 (z), and (4) define the problem as to its 

 position in the general theory of inheri- 

 tance, and (3) and (5) are the variables 

 whose interrelationship we wish to deter- 

 mine within the universe defined by (1), 

 (2.), and (4). To formulate the problem 



mathematically, the author defines inten- 

 sity of selection by the statement that 

 "if a generation of zygotes immediately 

 after fertilization consists of two pheno- 

 types A and B in the ratio pAliB, and the 

 proportion which forms a fertile union is 

 pA:(i-k~)B, we shall describe k as the 

 coefficient of selection". This index k 

 is used by the author to measure the 

 intensity of selection, and it may take 

 values between 1 and — 00 . At the ex- 

 tremes selection is complete, for when k = 

 i,noB's reproduce and when k = — 0° , no 

 A's reproduce. When k is small, selection 

 is slow; if k is positive, it is in favor of the 

 A's and if negative, in favor of the B's. 

 If the nth generation consists of types 



A and B in the ratio u n A:iB (or if the 



proportion of B's in the total universe is 



y n where y n = 



the problem 



1 + Un 



resolves itself into the determination of the 

 functional relationship between u n (or 

 jy„) and k, under different modes of inherit- 

 ance and different systems of breeding. 



All of the papers of this series are 

 concerned with the determination of such 

 functional relationships under a wide 

 variety of conditions, and the considera- 

 tion of some of the general conclusions 

 that follow from such an analysis. 



The first paper deals with some of the 



M5 



